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Systemic risk refers to the risk of collapse of an entire complex system as a result of the actions taken by the individual component entities or agents that comprise the system. Systemic risk is an issue of great concern in modern financial markets as well as, more broadly, in the management of complex business and engineering systems. We propose an axiomatic framework for the measurement and management of systemic risk based on the simultaneous analysis of outcomes across agents in the system and over scenarios of nature. Our framework defines a broad class of systemic risk measures that accomodate a rich set of regulatory preferences. This general class of systemic risk measures captures many specific measures of systemic risk that have recently been proposed as special cases and highlights their implicit assumptions. Moreover, the systemic risk measures that satisfy our conditions yield decentralized decompositions; i.e., the systemic risk can be decomposed into risk due to individual agents. Furthermore, one can associate a shadow price for systemic risk to each agent that correctly accounts for the externalities of the agent's individual decision making on the entire system. This paper was accepted by Gérard P. Cachon, stochastic models and simulation.

One of the best known and most widely referenced models for representing ordinal preferences is that due to Kemeny and Snell (Kemeny, J. G., L. J. Snell. 1962. Preference ranking: an axiomatic approach. Mathematical Models in the Social Sciences. Glnn, New York, 9–23.). This model is designed to accommodate pairwise comparison data with an l1 norm used to measure voter disagreement. While this model possesses many of the necessary properties for a social choice function, solution procedures developed to date have been capable of handling only small problems due to the difficulty of modelling the transitivity requirements of an optimal consensus ranking. This paper shows how the consensus formation problem for strict linear orderings can be modelled as a generalized network. Since efficient computer codes already exist for handling this special structure, this approach will permit the solution of much larger problems than has been the case previously.

This paper proposes a set of axioms for combining expert probability assessments. The axioms provide a framework for understanding previous results, and are used to derive a new method for combining event probabilities from different sources into a single estimate.

Morris proposed a set of axioms for combining experts’ probability assessments. It is here argued that one of these axioms is unsatisfactory. Its use leads to a conflict between the discrete and continuous cases which disappears in a coherent approach.

The focus of this paper is on determining appropriate combination rules for idiosyncratic ordinal utility functions in conjoint measurement. An axiomatic diagnosis is used which is based on explanatory criteria rather than goodness-of-fit or predictive criteria. Experimental results are presented comparing the selection of combination rules based on axiomatic tests and empirical fitting procedures for additive (x + y + z) and distributive (x(y + z)) combinations of three factors. A number of conflicting diagnoses result from the simultaneous applications of axiomatic tests and goodness-of-fit criteria, suggesting the importance of testing certain necessary conditions for simple polynomial combination rules, such as additive and distributive rules. Because the axiomatic approach is effective in rejecting inappropriate functional forms, we argue that it should complement rather than replace the empirical fitting diagnostic approaches.

Morris (Morris, P. A. 1983. An axiomatic approach to expert resolution. Management Sci. 29 24–32.) develops an axiom system for combining expert judgments by means of a processing rule. It is shown that the axioms are self-contradictory.

This paper discusses some current issues in the combination of probabilities and serves as an introduction to a series of four papers and a rejoinder relating to a paper by Morris (Morris, P. A. 1983. An axiomatic approach to expert resolution. Management Sci. 29 24–32.) on an axiomatic approach to expert resolution. The axiomatic approach and the modeling approach to expert resolution are discussed, and some comments on practical issues are given.

This paper presents an axiomatic approach to the problem of aggregating expert assessments of an event's probability into some group probability assessment. A multiplicative formula is derived.

In order to avoid the task of assessing a complicated likelihood function, Morris uses an axiomatic approach to develop a multiplicative rule for aggregating a decision maker's and an expert's probabilities. An essential shortcoming of the multiplicative rule is that it does not allow the decision maker to model his beliefs about the dependence between his assessment and the expert's. The root of the problem lies in the fact that the decision maker must calibrate the expert's information. When the calibration is done properly, the decision maker is forced to tackle the task which Morris proposes to avoid.